Watertown republican. [volume] (Watertown, Wis.) 1860-1906, 1887-03-16
THE EARTH'S CURVATURE.
An Illustration of Its Effect Upon the visi-
bility of Objects.

An Illustration of Its Effect Upon the visi-
bility of Objects.
The curvature OF the earth's surface
can not be perceived by the eye in
merely gazing upon it from an eleva-
ton; this is because the vision is not
capable of the comparison of height,
etc, necessary to perceive this curved
surface. But comparison of the height
of objects at various distances will
prove the fact of curvature plainly.
For a statute mile the curvature is 6.99
inches; for q geographical or nautical
mile it is 1862 inches. Its effect upon
the visibility of objects may be thus
illustrated. If a pane of glass is held
against a globe, the objects will touch
only at one point, the globes surface
continually falling away from the glass
Suppose the ocean to be calm and
frozen, and q great level sheet of glass
laid upon it. At one mile from the
tangent point the ocean falls nearly
eight inches below the glass, at three
miles six feet, at nine miles over fifty
feet, and so on. The number of feet
of depression is equal to two-thirds of
the square of the number of miles for
any observable distance. But in esti-
mating the visibility of objects it must
be noted that this depression is partial
ly cancelled by the phenomena of re-
fraction, which causes objects to APP
pear higher than they would if there
were no atmosphere. Careful measure
ments have shown that the error from
refraction averages rather more than
one-seventh of that from curvature.
The rule, therefore, commonly used
for correction of curvature and
refraction is: Square the number
the correction in feet. Thus, if an OBJ
iect is visible at a distance of five miles
we may know that its height is about
fourteen and one-tilird feet. Or if the
height of the visible object is known
say one hundred feet-take one-fourth
of this, multiply by seven, and take the
square root of this product, which gives
the distance of the object, in this case
q fraction over thirteen miles. The
error frequently made in computations
of this kind is that they do not take
into consideration the elevation of the
observer as well as that of the object
observed. A man swimming on the
surface of the water can perceive a
tower two hundred feet high and nine
teen miles away as a mere speck on the
horizon; but if the man were elevated
one hundred feet above the surface of
the water he could fully perceive a
tower half the height of the other on a
horizon fully twenty-six miles distant.
Very wild statements are often made
about the visibility of objects at great
distances. 1t is wisest not to believe
them until they have been tested by
observation and comparison with the
above rule. Thus the assertion has
been made that the electric light on the
Board of Trade building in Chicago,
three hundred feet above the level of
Lake Michigan, is visible eighty miles
distant. According to the above rule
an observing point to perceive the light
at this distance should be seventeen
hundred and twenty feet above the lake
level. We know of no point SO ele-
waited within one hundred miles of this
city. Therefore we exercise our right
of free judgment to doubt whether the
curvature of the earth is so greatly
overcome by the brilliancy of this
beautiful circle of electric light.-Chi-
cdg0 Inter Ocean.